There are a variety of simulations of waves in a stretched string.


  • This simulation from Andrew Duffy at Boston University illustrates standing and traveling waves in a string, and harmonics.


  • This simulation from Falstad illustrates standing waves on a string, with a breakdown of fourier harmonic magnitudes and phases. You can show the results from a transient plucking or an ongoing driving force, with variable tension and damping.


  • Dan Russell of Penn State offers animations and mathematical treatments of plucked, struck/hammered, and bowed strings.

Plucked (e.g. guitar):

Struck (e.g. piano):

Bowed (E.g. violin):


  • Russell also offers this comparison of strings and 2D membranes